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solve_projective.m
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solve_projective.m
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% Digital Video Stabilization and Rolling Shutter Correction using Gyroscopes
% Copyright (C) 2011 Alexandre Karpenko
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
function [ff td ts wd err] = solve_projective(gyro, frame_time, W, video_file)
gyro(:,[2 1]) = gyro(:,1:2); % x & y are swapped
gyro(:,3) = -gyro(:,3); % rotations about z
dft = diff(frame_time);
dT = diff(gyro(:,4));
theta = ((gyro(1:end-1,1:3) + gyro(2:end,1:3)) / 2) .* dT(:,[1 1 1]);
theta = [0 0 0; cumsum(theta, 1)];
ff = -1572;
td = -0.1564;
ts = 0;
alpha_f = 1e-12;
alpha_td = 1e-12;
alpha_ts = 1e-12;
alpha_wd = 1e-10;
wd = -mean(gyro(:,1:3),1);
%d = [0 0 0]; % gyro drift
% read corresponding movie
xyloObj = mmreader(['data/' video_file '.mov']);
num_frames = xyloObj.NumberOfFrames;
vh = xyloObj.Height;
vw = xyloObj.Width;
frame1 = read(xyloObj, 200);
frame2 = read(xyloObj, 201);
for iter = 1:5000
for f=100:num_frames-1
dE_df = 0;
dE_dtd = 0;
dE_dts = 0;
err = 0;
denom = 0;
x = W(f).x1;
y = W(f).x2;
for i = 1:size(x,1)
K = [1 0 -vw/2; 0 1 -vh/2; 0 0 ff];
X = K*[x(i,:)'; 1];
Y = K*[y(i,:)'; 1];
tx = frame_time(f) - td - ts * X(2) / vh;
ty = frame_time(f+1) - td - ts * Y(2) / vh;
w = interp1(gyro(:,4), gyro(:,1:3), [tx ty], 'linear', 'extrap');
dw = diff(w);
dws = (w(2,:) * Y(2) - w(1,:) * X(2)) / vh;
dth = diff(interp1(gyro(:,4), theta(:,1:3), [tx ty], 'linear', 'extrap'));
Rx = [1 0 0;
0 cos(dth(1)) -sin(dth(1));
0 sin(dth(1)) cos(dth(1))];
Ry = [ cos(dth(2)) 0 sin(dth(2));
0 1 0;
-sin(dth(2)) 0 cos(dth(2))];
Rz = [cos(dth(3)) -sin(dth(3)) 0;
sin(dth(3)) cos(dth(3)) 0;
0 0 1];
dRx =[0 0 0;
0 -sin(dth(1)) -cos(dth(1));
0 cos(dth(1)) -sin(dth(1))];
dRy =[-sin(dth(2)) 0 cos(dth(2));
0 0 0;
-cos(dth(2)) 0 -sin(dth(2))];
dRz =[-sin(dth(3)) -cos(dth(3)) 0;
cos(dth(3)) -sin(dth(3)) 0;
0 0 0];
R = Rz * Ry * Rx;
RY = R * Y;
XXY_XYX = X'*X*RY' - X'*RY*X';
dE_dts = dE_dts + 2 * (XXY_XYX) * (Rz * Ry * dRx * dws(1) + Rz * dRy * Rx * dws(2) + dRz * Ry * Rx * dws(3)) * Y;
dE_dtd = dE_dtd + 2 * (XXY_XYX) * (Rz * Ry * dRx * dw(1) + Rz * dRy * Rx * dw(2) + dRz * Ry * Rx * dw(3)) * Y;
dE_df = dE_df + 2*(RY'*RY)*X(3)*ff + 2*(X'*X)*(RY'*(R*[0;0;f])) - 2*(X'*RY)*(ff*RY(3) + X'*(R*[0;0;f]));
%{
if f == 200 && mod(iter-1,20) == 0
figure(1); clf;
h1 = imshow(frame2); hold on;
h2 = imshow(imtransform(frame1, maketform('affine', M'), 'XData', [1 vid_width], 'YData', [1 vid_height]));
set(h2, 'AlphaData', 0.6);
hold off;
pause(0.01);
end
%}
err = err + (X'*X)*(Y'*Y) - (X'*RY)^2;
denom = denom + 1;
end
err = err / denom;
ff = ff + alpha_f * dE_df;
%td = td - alpha_td * dE_dtd;
%ts = ts - alpha_ts * dE_dts;
fprintf('f: %f, td: %f, ts: %f, d: (%f, %f, %f), error: %f\n', ff, td, ts, 0, 0, 0, err);
end
end